Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Volume IV
Published on 15. May 2020
633 pages
978-1-5361-7475-5 (ISBN)
Description
The exponential growth of technology forces all disciplines to adjust accordingly, so they can meet the demands of a very dynamic world that heavily depends upon it. Therefore, mathematics cannot be an exception. In fact, mathematics should be the first to adjust and in fact it is. In this volume, which is a continuation of the previous three under the same title, we present state-of-the-art iterative methods for solving equations related to concrete problems from diverse areas such as applied mathematics, mathematical: biology, chemistry, economics, physics and also engineering to mention a few. Most of these methods are new and a few are old but still very popular. One major problem with iterative methods is that the convergence domain is small in general. We have introduced a technique that finds a smaller set than before containing the iterates leading to tighter Lipschitz functions than before. This way and under the same computational effort, we derive: weaker sufficient convergence criteria (leading to a wider choice of initial points); tighter error bounds on the distances involved (i.e., fewer iterates are needed to obtain a desired predetermined accuracy), and a more precise information on the location of the solution. These advantages are considered major achievements in computational disciplines. The volume requires knowledge of linear algebra, numerical functional analysis and familiarity with contemporary computing programing. It can be used by researchers, practitioners, senior undergraduate and graduate students as a source material or as a required textbook in the classroom.
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Ioannis K. Argyros
Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Volume IV
Book
05/2020
Nova Science Publishers Inc
€389.86
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Content
- Intro
- MATHEMATICAL MODELINGFOR THE SOLUTION OF EQUATIONSAND SYSTEMS OF EQUATIONS WITHAPPLICATIONSVOLUME IV
- MATHEMATICAL MODELINGFOR THE SOLUTION OF EQUATIONSAND SYSTEMS OF EQUATIONS WITHAPPLICATIONSVOLUME IV
- Contents
- Preface
- Chapter 1A Family of Cubically ConvergentMethods
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 2Characterization of SomeNewton-Like Methods
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 3Newton's Method Defined on NotNecessarily Bounded Domains
- 1. Introduction
- 2. Semilocal Convergence Analysis of Newton's Method
- Conclusion
- References
- Chapter 4Local Convergence of a Class ofMulti-Point Super-Halley Methods
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 5Ulm's-Like Method under WeakConvergence Conditions
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 6Newton-Like Method Free ofBilinear Operators
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 7On the Local Convergence of aSecant Like Method
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 8Extending the Applicability ofNewton's Method
- 1. Introduction
- 2. Analysis
- 3. Numerical Examples
- Conclusion
- References
- Chapter 9A Derivative Free Solver in BanachSpace
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 10Convergence for Two OptimalEighth-Order Methods
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 11Local Convergence of anEighth-Order Method
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 12An Efficient Class of Fourth-OrderJarratt-Type Methods
- 1. Introduction
- 2. Uni-Parametric Family of Jarratt-TypeMethodsand Convergence Analysis
- 3. Convergence Analysis
- 4. Special Cases
- 5. Local Convergence
- 6. Numerical Experiments
- References
- Chapter 13Unified Local Convergence for aCertain Family of Methods
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 14Ball Convergence for Eighth-OrderVariants of Hansen-Patrick's Family
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 15Extended Local Convergence ofNewton-Type
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 16Local Analysis of an Ostrowski-LikeMethod
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 17Local Convergence for MultipointMethods
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 18Choosing Good Starting Points forthe Convergence of Newton's Method
- 1. Introduction
- 2. Choosing Good Initial Points for Newton's Method (1.2)
- References
- Chapter 19Local Convergence of aTri-Parametric Eighth OrderMethod
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 20Ball Convergence for Ostrowski-LikeMethod with AcceleratedEighth-Order Convergence
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 21A Traub-Steffensen-LikeComposition for BanachSpace Valued Operators
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Example
- References
- Chapter 22A Novel Traub-Steffensen Three-StepIterative Method Free of Derivates
- 1. Introduction
- 2. Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 23Extended Semilocal Convergence ofthe NHSS Method under GeneralizedLipschitz Condition
- 1. Introduction
- 2. Newton-HSSMethod
- 3. Preliminaries
- 4. Semi-Local Convergence Theorem
- References
- Chapter 24A Novel Traub-Steffensen Three StepIterative Method Free of Derivates
- 1. Introduction
- 2. Convergence I: Smooth Equations
- 3. Convergence II: Nonsmooth Equations
- References
- Chapter 25Extended Local Convergence of anEfficient Sixth-Order Method
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 26Traub-Steffensen-Type Solvers forNonlinear Equations
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 27Unified Local Convergence forThird-Order Methods
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 28Improved Error Bounds forNewton-Type Solvers - I
- 1. Introduction
- 2. Semi-Local Convergence
- 3. Extensions to Other Solvers
- 4. Specializations to Newton's Solver
- References
- Chapter 29Improved Error Bounds forNewton-Type Solvers - II
- 1. Introduction
- 2. Semi-Local Analysis
- References
- Chapter 30Comparing the ExtendedYamamoto's Error Boundsfor Newton's Solver
- 1. Introduction
- 2. Recurrence Relation and Majorant Principle
- References
- Chapter 31Extended Newton's Method forNonsmooth Operators
- 1. Introduction
- 2. Convergence
- References
- Chapter 32Extended and Unified ConvergenceTheory for Iterative Processes
- 1. Introduction
- 2. Convergence Analysis
- 3. Approximate Newton Processes
- References
- Chapter 33Comparison of Two Sixth-OrderSolvers Using the First Derivative
- 1. Introduction
- 2. Local Convergence ofMethod (33.2)
- 3. Local Convergence of Solver (33.3)
- 4. Numerical Examples
- References
- Chapter 34Efficient Third Convergence OrderMethod for Solving NonlinearSystems
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 35On the Local Convergence of anEfficient Third Convergence OrderMethod
- 1. Introduction
- 2. Local Convergence Analysis
- 3. Numerical Examples
- References
- Chapter 36Extended Convergence forNewton-Like Solvers
- 1. Introduction
- 2. Semi-Local Convergence
- References
- Chapter 37Ball Convergence of Schr¨oder-LikeMethods for Multiple Roots
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 38Ball Convergence of Eighth-OrderMethods for Multiple Roots
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 39Fourth-Order Newton-Type Methodsfor Roots of Multiplicity
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 40Gauss-Newton Solvers withProjections for SolvingLeast Squares Problems
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 41Extended Ball Convergence Resultsfor Newton's Solver underH¨older-Like Conditions
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 42Ball Convergence forTraub-Steffensen-Chebyshev Solver
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 43Extended Ball Convergence of theGauss-Newton Solverfor Injective-OverdeterminedSystems of Equations
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 44Extended Ball Convergence forNewton Conditional Gradient Solver
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 45Extended Ball Convergence of theGauss-Newton-Like Solver forInjective-Overdetermined Systemsof Equations
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 46Extended Ball Convergence forInexact Newton-Like ConditionalGradient Solver
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 47Extended Ball Convergence of theGauss-Newton Solver
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 48Extended Semi-Local Convergence ofthe Gauss-Newton Solver for ConvexComposite Optimization
- 1. Introduction
- 2. Semi-Local Convergence
- References
- Chapter 49Extended Local ConvergenceAnalysis of a ProximalGauss-Newton Procedure
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 50Extended Local Convergence of theGauss-Newton Method
- 1. Introduction
- 2. Ball Convergence
- References
- Chapter 51Solvers for Problems with SmallDivisors
- 1. Introduction
- 2. Convergence Analysis
- References
- Chapter 52A Two-Step Iterative Scheme with aFree Parameter
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 53A Family of Unified HighConvergence Order Methods
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 54Three Step Seventh-Order Methodfor Solving Equations
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 55A Unified Family of Jarratt-LikeIterative Methods in Banach Space
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Examples
- References
- Chapter 56Extended Local Convergence forNewton Simpson's 3/8th Solver
- 1. Introduction
- 2. Local Convergence I
- 3. Local Convergence II
- 4. Numerical Example
- References
- Chapter 57On the Harmonic Mean andMidpoint Newton's Solver
- 1. Introduction
- 2. Local Convergence of HMNS
- 3. Local Convergence ofMNS
- 4. Numerical Example
- References
- Chapter 58Comparing the Local Convergence ofThree Newton-Mean-Type Solvers
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Example
- References
- Chapter 59Comparing Two High ConvergentOrder Methods
- 1. Introduction
- 2. Convergence Analysis
- 3. Numerical Example
- References
- Chapter 60Generalized Solvers for Equations
- 1. Introduction
- 2. Convergence Analysis
- References
- Chapter 61On the Harmonic Mean andMidpoint Newton's Solver - II
- 1. Introduction
- 2. Local Convergence of HMNS
- 3. Numerical Example
- References
- Chapter 62Extended Jarratt-Type Solver
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Example
- References
- Chapter 63Extended Chebyshev-Type Solverwithout Second Derivates
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Example
- References
- Chapter 64Newton-Type Solvers UsingFifth-Order Quadrature Formulas
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Example
- References
- Chapter 65Extending the Local Convergence ofan Efficient Sixth-Order Method
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Example
- References
- Chapter 66Increased and Extended LocalConvergence for Some IterativeMethods
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Example
- References
- Chapter 67Extended Newton-Traub-TypeMethods
- 1. Introduction
- 2. Local Convergence
- 3. Numerical Example
- References
- Chapter 68Extended Newton-Traub Methods
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 69Solvers of Convergence Three andFour with a Free Parameter
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 70Extended Fourth-Order WeightedNewton Solver
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 71Extended Sixth-Order Schemes withParameters
- 1. Introduction
- 2. Convergence Analysis
- References
- Chapter 72Extended Newton-Jarratt Scheme
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 73Chebyshev-Halley-Type Methodswith Parameters
- 1. Introduction
- 2. Convergence Analysis
- References
- Chapter 74Ostrowski-Chun Like Schemes withParameters
- 1. Introduction
- 2. Convergence Analysis
- References
- Chapter 75Extended Seventh-Order Methodwith Divided Differences
- 1. Introduction
- 2. Convergence Analysis
- References
- Chapter 76Derivative-FreeMethods I: OrderSix
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 77Derivative-FreeMethods II: OrderSeven
- 1. Introduction
- 2. Local Convergence
- References
- Chapter 78High-Order and Efficient Solvers inBanach Spaces
- 1. Introduction
- 2. Convergence Analysis
- References
- Chapter 79Derivative Free Method III: OrderSeven
- 1. Introduction
- 2. Convergence Analysis
- References
- Chapter 80Derivative Free Method IV: OrderSix
- 1. Introduction
- 2. Convergence Analysis
- References
- Chapter 81Extended Semilocal Convergence of aSixth-Order Jarratt-Type Methodin Banach Space
- 1. Introduction
- 2. Semi-Local Convergence
- 3. Semi-Local Convergence
- References
- Chapter 82Extended Inexact Gauss-NewtonLike Schemes for InjectiveOverdetermined Equations
- 1. Introduction
- 2. Local Convergence Analysis for IGNLS
- References
- About the Authors
- Index
- Blank Page
